Though Bottom often steals the show in performance, Puck is usually considered the most important character in A Midsummer Night’s Dream.
Comparing Puck to Bottom, why might Puck be considered the protagonist?
There is a good bit of evidence to support the premise that Puck is the protagonist in Shakespeare's Midsummer Night's Dream, despite the fact that Bottom does steal the show. However, if Puck had not decided to turn Bottom into an ass in the first place, he might never have caught the attention of the Fairy Queen and had the opportunity to be such an important player in the affairs of Oberon and Titania's court. Both Puck and Bottom are different than the other characters in that they actually interact with characters in both the fairy and mortal realms. Puck's actions drive the plot as soon as the humans intrude on the fairy gathering in the forest; he is Oberon's henchman, but he acts independently as well, and he is the comic mover of the action of the play.
Moreover, Shakespeare gives Puck the final speech in the epilogue, which is usually reserved for the main protagonist, for example, Rosalind in As You Like It, another indication of his importance in the play.
If you are considering a Comedy structurally, then neither Puck nor Bottom is the protagonist. Both are characters whose actions (Puck) contribute to the complications of the main plot or whose actions (Bottom) comprise a subplot that comments on the characters/events of the main plot. Since neither's actions are actually the driving force of the main plot, neither can be considered the protagonist. So, who then, is the protagonist?
Classically, a comedy must end in at least one marriage, and it is the central character(s), the protagonist(s) who go(es) through the main trials and tribulations of the play, only to have all ironed smoothly out for the "happy" ending in marriage.
One such charcter is Hermia. She begins the play in a dilemma (similar to a dilemma Juliet faces in Romeo and Juliet). She wants to marry for love to Lysander, but her father wants her to marry Demetrius. She is given an order to marry Demetrius or else suffer the consequences -- be killed (!!) or join a nunnery. She decides to flee to the forest with Lysander.
There is also a case to be made for Helena as a protagonist, since she is in love with Demetrius at the beginning of the play, and creates a plan to alert him to Lysander and Hermia's scheme and then follow him, hoping to win back his love.
A great deal of the mischief and mix-up in the play revolves around the young lovers' story lines. As a group, they could be considered the protagonists, or you could make a case, as I have done above, for one of them. And, as is traditional in Shakespeare's comedies, there is a subplot invoving low-born characters, the clowns, who are in the play to entertain the audience in the very ways you describe. They are often the ones who "steal the show." But this does not make them the protagonists of the story.
Bottom is the foil, Puck is the classic trickster. The trickster character is generally a messenger to the gods or for the gods whose amorality and desire to "play" often serve as the catalyst for events that are set into motion. These, in drama, are usually humorous in nature such as the mistaken identities and mixed up outcomes that prevail in "Midsummer Night's Dream". Puck is the driving force for all of the action as well as the conscience of the characters (both the good side and the bad side). As such, it is definitely possible to argue for is role as the protagonist around whose actions the story revolves. As he closes the play, his final monologue begs the audience's forgiveness and wishes them well for having been participant's in Pucks dream or vision, so again it all springs forth from Puck.